In PET imaging, or positron emission tomography, a radiopharmaceutical agent is administered, via injection, inhalation and/or ingestion, to a patient. The physical and bio-molecular properties of the agent then concentrate at specific locations in the human body. The actual spatial distribution, intensity of the point and/or region of accumulation, as well as the kinetics of the process from administration and capture to eventual elimination, all have clinical significance. During this process, the positron emitter attached to the radiopharmaceutical agent emits positrons according to the physical properties of the isotope, such as half-life, branching ratio, etc. Each positron interacts with an electron of the object, is annihilated and produces two gamma rays at 511 keV, which travel at substantially 180 degrees apart. The two gamma rays then cause a scintillation event at a scintillation crystal of the PET detector, which detects the gamma rays thereby. By detecting these two gamma rays, and drawing a line between their locations or “line-of-response,” the likely location of the original annihilation is determined. While this process only identifies one line of possible interaction, accumulating a large number of these lines, and through a tomographic reconstruction process, the original distribution is estimated with useful accuracy. In addition to the location of the two scintillation events, if accurate timing—within a few hundred picoseconds—is available, time-of-flight calculations are also made in order to add more information regarding the likely position of the annihilation event along the line. Limitations in the timing resolution of a scanner determine the accuracy of the positioning along this line. Limitations in the determination of the location of the original scintillation events determine the ultimate spatial resolution of the scanner. A specific characteristic of the isotope (for example, energy of the positron) contributes (via positron range and co-linearity of the two gamma rays) to the determination of the spatial resolution for a specific radiopharmaceutical agent.
The above process is repeated for a large number of annihilation events. While every case needs to be analyzed to determine how many scintillation events are required to support the desired imaging tasks, conventionally a typical 100 cm long, FDG (fluoro-deoxyglucose) study accumulates about 100 million counts or events. The time required to accumulate this number of counts is determined by the injected dose, as well as the sensitivity and counting capacity of the scanner.
PET imaging relies on the conversion of gamma rays into light through fast and bright scintillation crystals, generating the scintillation events referred to above. Time-of-Flight (ToF) PET further requires sub-nanosecond timing resolution and resolutions of a few hundred picoseconds is also being contemplated. While it is complicated enough to tune and adjust two channels of scintillating crystal, photomultiplier tubes (PMT), and electronics, this complexity is only increased on a large arrays of crystals and sensors.
Modern PET systems support 500-600 ps timing resolutions.
Conventionally, arrival time determination of PMT output signals is difficult to achieve with significant accuracy because of the limitations of discrete elements. Moreover, with current ADC sample rate technology, only a small number of samples will fall within the leading edge of the PMT output signal, thus providing low-quality time stamp determination.
In addition, certain methods have been used to attempt to extract timing information from waveforms that are undersampled. For example, average functions for prototype functions and theoretically derived weighting or filter functions have been used. The average function is a close guess for the prototype function, but one significant problem is that the averaging process will invariably add blurring to the very leading edge of the pulse, where the most critical timing information is contained. The filter coefficients used in optimal filter approaches have been based on mathematical formulations which derive the weighting functions from the covariance matrix.